Mathematics Seminar: "Coalescence in branching processes"
4:10pm Neill 5W
Krishna B. Athreya
Take rooted tree. Go to the nth level. Pick two vertices at random by SRSWOR. Trace their lines of descent back till they meet. Call that level Xn. In this talk we investigate the probability distribution of Xn and its weak limit as n goes to infinity for trees generated by Galton Watson branching processes. We consider single type branching processes for all four cases, namely super critical, subcritical, critical and explosive. We give an application of this to branching random walks.
This is an analysis seminar that will be given in a colloquium style.